Why the common view about this institution is misguided
The current way a lot of American progressives think of the Supreme Court only dates back to Brown vs. the Board. Before that the progressive left was actually deeply suspicious of judicial review (which Brown dramatically expanded).
I wouldn't say the trouble distinguishing between outcomes and process has to do with being left or right. Activists and the public across the spectrum tend to focus on the outcome. It has more to do with how the Constitution is romanticized into an expression of national identity. I think the reality is the actual text is often ambiguous and subject to more than one defensible interpretation (substantive due process being a great example).